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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A necessary and sufficient condition for Ricci shrinkers to have positive AVR
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by Bennett Chow, Peng Lu and Bo Yang PDF
Proc. Amer. Math. Soc. 140 (2012), 2179-2181 Request permission

Abstract:

In this short paper we observe that a recent result of C.-W. Chen meshes well with earlier work of H.-D. Cao and D.-T. Zhou, O. Munteanu, J. Carrillo and L. Ni, and S.-J. Zhang. We give a necessary and sufficient condition for complete noncompact shrinking gradient Ricci solitons to have positive asymptotic volume ratio.
References
  • Huai-Dong Cao and Detang Zhou, On complete gradient shrinking Ricci solitons, J. Differential Geom. 85 (2010), no. 2, 175–185. MR 2732975
  • Carrillo, José A., Ni, Lei, Sharp logarithmic Sobolev inequalities on gradient solitons and applications. Communications in Analysis and Geometry 17 (2009), 721–753.
  • Bing-Long Chen, Strong uniqueness of the Ricci flow, J. Differential Geom. 82 (2009), no. 2, 363–382. MR 2520796
  • Chen, Chih-Wei, On the injectivity radius and tangent cones at infinity of gradient Ricci solitons. arXiv:1012.1217.
  • Fu-quan Fang, Jian-wen Man, and Zhen-lei Zhang, Complete gradient shrinking Ricci solitons have finite topological type, C. R. Math. Acad. Sci. Paris 346 (2008), no. 11-12, 653–656 (English, with English and French summaries). MR 2423272, DOI 10.1016/j.crma.2008.03.021
  • Haslhofer, Robert, Müller, Reto, A compactness theorem for complete Ricci shrinkers. arXiv:1005.3255v2.
  • Munteanu, Ovidiu, The volume growth of complete gradient shrinking Ricci solitons. arXiv:0904.0798.
  • Zhang, Shijin. On a sharp volume estimate for gradient Ricci solitons with scalar curvature bounded below. arXiv:0909.0716, Acta Mathematica Sinica 27, no. 5 (2011), 871–882.
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Additional Information
  • Bennett Chow
  • Affiliation: Department of Mathematics, University of California San Diego, La Jolla, California 92093
  • MR Author ID: 229249
  • Email: benchow@math.ucsd.edu
  • Peng Lu
  • Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403
  • MR Author ID: 308539
  • Email: penglu@uoregon.edu
  • Bo Yang
  • Affiliation: Department of Mathematics, University of California San Diego, La Jolla, California 92093
  • Email: b5yang@math.ucsd.edu
  • Received by editor(s): February 2, 2011
  • Published electronically: September 30, 2011
  • Communicated by: Jianguo Cao
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 140 (2012), 2179-2181
  • MSC (2010): Primary 53Cxx
  • DOI: https://doi.org/10.1090/S0002-9939-2011-11173-0
  • MathSciNet review: 2888203